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In this section you can see my introductory notes on Fractional Calculus. You can also download them in pdf format at the downloads section.

Our understanding of Nature relies on calculus, which in turn relies on the intuitive concept of the derivative. It's descriptive power comes from the fact that it analyses the behavior at scales small enough that its properties change linearly, so avoiding complexities that arise at larger ones. Fractional Calculus generalizes this concept from integer to non-integer order. Despite it seems not to have significant applications in fundamental physics, research on this core concept could be valuable in understanding Nature. These notes comprise an introduction to the field.

  1. Introduction
  2. Exponentials
  3. Powers
  4. Binomial Formula
  5. Functions of the Derivative
  6. Grunwald-Letnikov Derivative
  7. Riemann-Liouville Derivative
  8. Domain Transforms
  9. Convolution
  10. Cauchy Integral Formula
  11. Properties
  12. Local Operators